Answer:
(a) v = 1.54m/s, (b) Θ = 80.6° and (c) E = 52.92J
Explanation:
(a) <u>At the lowest point, the total energy is giving by:</u>
<em>where,: kinetic energy,: potential energy, m: pendulum's mass, v: speed of the pendulum, g:gravity and y: heigh of the pendulum. </em>
(1)
<u>When the string is at 64° from the vertical, the total energy is:</u>
(2)
<u>At this point, is:</u>
(3)
<em>where L: longitude of the pendulum </em>
By conservation of energy, we can calculate the speed of the string, at 64 ° to the vertical. Equaling equations (1) and (2):
(b) <u>Smilarly, by conservation of energy we can find the greatest angle, assuming that vf = 0 at the greatest angle reached</u>:
Using the heigh calculated in equation (3) we can find the angle:
(c) The total mechanical energy at the lowest point is giving by:
Have a nice day!